Blackboard Shots with Prefix "Afeke"

240913-142411: Proof of the stitching formula (2).

240913-142410: Proof of the stitching formula.

240411-104531: Unitarity for tangles (11).

240226-115654: Unitarity for tangles (10).

240202-112547: Unitarity for tangles (9).

240124-110022: Unitarity for tangles (8).

240117-113209: Unitarity for tangles (7).

240112-113439: Unitarity for tangles (6).

231106-143156: Unitarity for tangles (5).

231020-132732: Unitarity for tangles (4).

231020-132003: Unitarity for tangles (3).

231006-111847: Unitarity for tangles (2).

230926-112555: Unitarity for tangles.

221214-121653: The homology reduced Gassner representation.

221207-131543: Intersection numbers in twisted homology (9).

221128-125305: Intersection numbers in twisted homology (8).

221121-125616: Intersection numbers in twisted homology (7).

221118-081503: Intersection numbers in twisted homology (6).

221109-115137: Intersection numbers in twisted homology (5).

221107-115534: Intersection numbers in twisted homology (4).

221031-132935: Intersection numbers in twisted homology (3).

221031-132930: Intersection numbers in twisted homology (2).

221031-132915: Intersection numbers in twisted homology.

221019-115945: $\Gamma$-calculus (8).

221019-113952: $\Gamma$-calculus (7).

221003-131518: $\Gamma$-calculus (6).

221003-125053: $\Gamma$-calculus (5).

220929-132009: $\Gamma$-calculus (4).

220920-131331: $\Gamma$-calculus (3).

220908-135316: $\Gamma$-calculus (2).

220906-115552: $\Gamma$-calculus.

220823-121143: Unitarity for groupoid representations (5).

220816-113312: Unitarity for groupoid representations (4).

220816-111340: Unitarity for groupoid representations (3).

220816-105958: Unitarity for groupoid representations (2).

220816-104557: Unitarity for groupoid representations.

220809-104022: Gassner as a functor (3).

220804-130344: Gassner as a functor (2).

220804-125927: Gassner as a functor.

220606-144534: Gassner for a single crossing.

220316-140256: LinAlg issue.

211214-122202: Recovering Gassner from $H_1$ (3).

211214-115545: Recovering Gassner from $H_1$ (2).

211130-172819: Recovering Gassner from $H_1$.

211123-165941: On to tangles! (5)

211123-164720: On to tangles! (4)

211123-161727: On to tangles! (3)

211116-164408: On to tangles! (2)

211116-163123: On to tangles!

211102-155035: The structure of the cup-product matrix (9).

211026-153454: The structure of the cup-product matrix (8).

211019-154103: The structure of the cup-product matrix (7).

211012-153813: The structure of the cup-product matrix (6).

211005-153836: The structure of the cup-product matrix (5).

210928-160007: The structure of the cup-product matrix (4).

210928-154030: The structure of the cup-product matrix (3).

210921-160425: The structure of the cup-product matrix (2).

210914-164623: The structure of the cup-product matrix.

210701-170112: Completing the Kirk argument (6).

210701-170111: Completing the Kirk argument (5).

210701-170110: Completing the Kirk argument (4).

210630-113540: Supervisory Meeting (2).

210630-113539: Supervisory Meeting.

210624-165821: Completing the Kirk argument (3).

210624-165820: Completing the Kirk argument (2).

210624-165819: Completing the Kirk argument.

210604-195914: Computing cup products (4).

210528-110135: Computing cup products (3).

210528-104400: Computing cup products (2).

210517-100249: Computing cup products.

210507-092613: More cohomology computations (5).

210507-092100: More cohomology computations (4).

210507-091439: More cohomology computations (3).

210429-152437: More cohomology computations (2).

210415-160909: More cohomology computations.

210208-164014: Cap products (2).

210208-163929: Cap products.

201211-153735: The twisted homology of $\partial X$.

201105-173823: Reading Kirk's email (2).

201105-170312: Reading Kirk's email.

201020-161550: Homological representations (2).

201020-161519: Homological representations.

200811-165033: A split sequence?

200729-155915: Crash recovery.

200724-160451: A crucial statement in Kassel-Turaev (6).

200720-154713: A crucial statement in Kassel-Turaev (5).

200720-154633: A crucial statement in Kassel-Turaev (4).

200715-155330: A crucial statement in Kassel-Turaev (3).

200709-173838: A crucial statement in Kassel-Turaev (2).

200703-160731: A crucial statement in Kassel-Turaev.

200626-132922: $H_1({\mathbb R}^2,{\mathbb Z}^2)$.

200626-132921: The map $\pi_1\to H_1$ is homomorphic (3).

200617-134608: The map $\pi_1\to H_1$ is homomorphic (2).

200615-153139: The map $\pi_1\to H_1$ is homomorphic.

200610-170726: Back to $\tilde{H}$ (7).

200610-170702: Back to $\tilde{H}$ (6).

200608-155824: Back to $\tilde{H}$ (5).

200601-153318: Back to $\tilde{H}$ (4).

200527-160353: Back to $\tilde{H}$ (3).

200525-154821: Back to $\tilde{H}$ (2).

200525-154403: Back to $\tilde{H}$.

200518-155434: The n-puncture case.

200513-170219: The relations between the $\alpha_n$'s (2).

200513-170218: The relations between the $\alpha_n$'s.

200504-150105: The Abelianization of a kernel (6).

200429-163709: The Abelianization of a kernel (5).

200423-171420: The Abelianization of a kernel (4).

200423-171419: Implementing Fox derivatives.

200417-170148: Back to $\tilde{H}$.

200417-170053: The Abelianization of a kernel (3).

200417-165539: The Abelianization of a kernel (2).

200415-170946: The Abelianization of a kernel.

200411-144200: $\tilde{H}$ in Kassel-Turaev 3.2.1 (2).

200407-152413: $\tilde{H}$ in Kassel-Turaev 3.2.1.

200404-150338: Relative homology (2).

200404-150149: Relative homology.

200330-160014: Back to Kassel-Turaev 3.2.1 (3).

200330-155613: Back to Kassel-Turaev 3.2.1 (2).

200330-152542: Back to Kassel-Turaev 3.2.1.

200328-154555: The intersection form (2).

200328-153721: The intersection form.

200327-160234: The boundary of an intersection (2).

200324-154112: The boundary of an intersection.

200320-161700: Kassel-Turaev Section 3.2.1 (2).

200320-155143: Kassel-Turaev Section 3.2.1.

200311-190547: Reading Kirk's email (3).

200311-190226: Reading Kirk's email.

200311-190225: Reading Kirk's email (2).

200305-175134: Poincare Duality (2).

200303-165933: Poincare Duality.

200226-131424: Supervisory meeting.

200217-151739: Poincare duality (6).

200217-145718: Poincare duality (5).

200211-131421: Poincare duality (4).

200211-131325: Poincare duality (3).

200211-131236: Poincare duality (2).

200211-131200: Poincare duality.

200211-130942: Compositions in homological representations.

200204-121538: Computing the braid action.

200128-131445: A basis for $H^1(X_0,p;F)$ (7).

200122-130202: A basis for $H^1(X_0,p;F)$ (6).

200122-125435: A basis for $H^1(X_0,p;F)$ (5).

200122-123958: A basis for $H^1(X_0,p;F)$ (4).

200113-095920: A basis for $H^1(X_0,p;F)$ (3).

200113-095732: A basis for $H^1(X_0,p;F)$ (2).

200113-094125: A basis for $H^1(X_0,p;F)$.

200108-124443: Recovering Gassner.

191218-143753: KLW Lemma 2.1 (4).

191218-141338: KLW Lemma 2.1 (3).

191212-124601: KLW Lemma 2.1 (2).

191212-124044: KLW Lemma 2.1.

191212-122710: KLW proposition 2.3 (5).

191127-143639: KLW proposition 2.3 (4).

191127-142330: KLW proposition 2.3 (3).

191122-122727: KLW proposition 2.3 (2).

191122-120738: KLW proposition 2.3.

191122-115709: Homology with local coefficients (9).

191122-114933: Homology with local coefficients (8).

191119-143238: Homology with local coefficients (7).

191113-131640: Homology with local coefficients (6).

191111-135011: Homology with local coefficients (5).

191111-133731: Homology with local coefficients (4).

191111-131110: Homology with local coefficients (3).

191029-190114: Homology with local coefficients.

191029-185533: Homology with local coefficients (2).

191024-190322: String links and homotopy.

191017-190302: Back to Burau! (2)

191017-185709: Back to Burau!

191017-184327: The chain rule in free groups (13).

191017-183549: The chain rule in free groups (12).

191010-192125: The chain rule in free groups (11).

191010-191543: The chain rule in free groups (10).

191010-184437: The chain rule in free groups (9).

191003-192708: The chain rule in free groups (8).

190930-184527: The chain rule in free groups (7).

190930-184112: The chain rule in free groups (6).

190930-181243: The chain rule in free groups (5).

190923-184744: The chain rule in free groups (4).

190923-181359: The chain rule in free groups (3).

190916-184930: The chain rule in free groups (2).

190916-182333: The chain rule in free groups.

190827-154127: The Burau representation (5).

190816-160159: The Burau representation (4).

190816-155111: The Burau representation (3).

190816-153738: The Burau representation (2).

190816-151604: The Burau representation.

190812-163442: The intuition behind combing (3).

190628-163014: The intuition behind combing (2).

190627-154010: The intuition behind combing.

190625-160848: Identifying $U_{n+1}$ (3).

190624-142251: Identifying $U_{n+1}$ (2).

190621-145402: Identifying $U_{n+1}$.

190621-143519: Semi-direct products (3).

190617-163131: Semi-direct products (2).

190617-162401: Semi-direct products.

190614-162610: Combing braids.

190612-165447: The Artin representation (2).

190612-163621: The Artin representation.

190607-145027: The Wirtinger presentation (3).

190606-145456: The Wirtinger presentation (2).

190603-154606: The Wirtinger presentation.

190603-153211: Braids and automorphisms of the free group (3).

190521-175423: Braids and automorphisms of the free group (2).

190517-153121: Braids and automorphisms of the free group.

190513-153437: Configuration space (3).

190513-152238: Configuration space (2).

190509-153548: Configuration space.

190507-173236: Braid groups (4).

190507-172228: Braid groups (3).

190507-170558: Braid groups (2).

190503-153151: Braid groups.

181119-155135: Rotation numbers.

180926-172206: Topological manifolds.

180919-180404: $SL(n)$ is a manifold.

180919-172936: Two patches for $S^1$.

180912-193411: A non-Hausdorff near-manifold (2).

180912-185856: A non-Hausdorff near-manifold.

180904-180351: The Seifert matrix (5).

180904-171431: The Seifert matrix (4).

180828-174029: The Seifert matrix (3).

180828-172554: The Seifert matrix (2).

180820-183658: The Seifert matrix.

180815-193444: The Seifert algorithm.

180807-164117: Surfaces and caravans.

180731-165422: A proof of R3?

180712-163148: Figuring our equivalence classes.

180704-182703: Back to Alexander.

180704-175450: Dehn and Wirtinger.

180625-173523: Finding the faces.

180619-170744: The Dehn presentation.

180619-164925: The Alexander module.

180619-163122: From edges to faces.

180613-170456: Invariance of Alexander's Alexander (2).

180613-164244: Invariance of Alexander's Alexander.

180613-163316: Implementing Alexander's Alexander.

180613-161721: Face-virtual knots.

180528-172914: Alexander's Alexander polynomial (2).

180528-172005: Alexander's Alexander polynomial.

171109-165132: Finitely generated Abelian groups and Gaussian elimination.

171030-165027: Distributing cows (4).

171017-181218: From triangulations to trees.

171010-184222: Tilings.

171004-173750: Distributing cows (3).

171004-171718: Distributing cows (2).

170929-171750: Cutting the plane by straight lines.

170929-164520: Distributing cows.

170925-180255: Sylow (3).

170925-175119: Sylow (2).

170922-180430: Sylow.