© | Dror Bar-Natan: Academic Pensieve: Blackboard Shots: Random

Blackboard Shots with Prefix "Chterental"


170407-144452: Morse isotopies.

170407-142215: OU tangles.

170124-172233: Brunnian 2-links.

170124-165749: The perforate map.

170124-163313: Branch point free Roseman theory.

170124-161109: The Yoshikawa moves.

160518-144411: The Goeritz group.

160518-142908: The Burnside $B(2,5)$ group and the Goeritz group.

160518-141647: On GPV.

160518-135452: Brunnian 2-component 2-links (2).

160505-142127: Brunnian 2-component 2-links.

160505-133641: A surjection from the free group to knot theory (3).

160505-133230: A surjection from the free group to knot theory (2).

160505-132926: A surjection from the free group to knot theory.

160505-132044: Two linked unknots have a good projection.

150616-140007: 1324-avoiding permutations.

150519-170656: The $\gamma_{ij}$ representation.

150512-154513: The fundamental group of the trefoil is a braid group.

150416-154651: MacMahon's formula (2).

150407-165500: MacMahon's formula.

150320-151053: Mapping flat braids to w-braids with $2n$ strands.

150320-145559: Artin'.

150320-144036: Braids on the annulus.

150305-170952: Canonical forms for curves on surfaces (3).

150305-170255: Canonical forms for curves on surfaces (2).

150223-140318: Canonical forms for curves on surfaces.

150129-170351: A possible canonical form for knots.

150129-163655: A simplified faithfulness proof.

150108-175300: The Swidler notation.

141219-150025: Quandles and Hopf words.

141219-143333: Combing at the curve-diagram level.

141212-144156: zhe on the level of arrow diagrams.

141113-160254: The Bardakov representation in a tiny rectangle.

141104-153628: Converting homotopies to isotopies. (more...)

141017-125012: Tethering.

140910-173507: $f:vB_n\times I_n\to vB_n$.

140828-172551: The Goeritz Group.

140820-084428: Modifying the Bardakov representation (2) - corrected.

140819-170409: Modifying the Bardakov representation (2). (more...)

140819-164542: Modifying the Bardakov representation.

140801-115534: $VB_n$ acts faithfully...

140725-113934: A random problem.

140703-180804: New reduction rules.

140626-162744: About Gassner (2).

140626-161545: About Gassner.

140619-132006: Towards automaticity of $B_n$ (2).

140619-130939: Towards automaticity of $B_n$.

140604-162357: The definition of automatic groups.

140521-140708: Acting on the left (2).

140521-133625: Acting on the left.

140515-142755: A case of the diamond lemma.

140515-135757: Diamond lemma preamble.

140515-133952: The Goeritz groups.

140515-133414: A 2-ring trick.

140507-140037: More on Harer-Zagier.

140507-133658: Groupings.

140430-134453: Simple decker sets to w-knots, also on the infinitesimal level.

140422-105652: Harer-Zagier (4).

140422-104316: Harer-Zagier (3).

140422-103839: Harer-Zagier (2).

140422-103252: Harer-Zagier.

140320-153436: Being parallel.

140313-151042: Planar matchings (3).

140313-145834: Planar matchings (2).

140313-144623: Planar matchings.

140306-150211: Well-definededness of the action.

140211-151202: The virtual fundamental meta-group (2).

140206-132404: The virtual fundamental meta-group.

140206-114427: Trying to show that v-braids inject into v-tangles.

140128-115104: R2 and R3 for virtual curve diagrams.

140114-124447: A step by step plan.

131216-150717: The case of ordinary braids (3).

131216-145741: The case of ordinary braids (2).

131216-143348: The case of ordinary braids.

131112-105420: Manturov's representation of the virtual braid group (4).

131112-104356: Manturov's representation of the virtual braid group (3).

131112-102024: Manturov's representation of the virtual braid group (2).

131112-101459: Manturov's representation of the virtual braid group.

131012-120842: Braids and graphs (2).

131012-113819: Braids and graphs.

130926-163426: Semi-group actions.

130910-153816: $\sigma$-diagrams.

130826-153829: The braid group is automatic?

130801-163852: Proving the injectivity of Artin's representation.

130801-162437: The diamond lemma.

130715-154812: Artin systems and v-Artin systems (5).

130715-153416: Artin systems and v-Artin systems (4).

130705-160009: Artin systems and v-Artin systems (3).

130702-154659: Artin systems and v-Artin systems (2).

130621-155855: Artin systems and v-Artin systems.

130621-153629: v-braids and Hopf words (2).

130614-114754: v-braids and Hopf words.

130614-110918: Planar representations of braids (2).

130614-103402: Planar representations of braids.

130610-160754: Round flat knots.

130509-153910: The free group modulo the braid group.

130506-170221: Long virtual knots.

130506-164120: Conjugacy classes in F_n modulo braid actions.

130506-154354: Bracelets.

130506-153345: Unknotting operation in 4D.

130422-151722: 2 simple curves = chord diagrams.

130401-172059: SC meeting.

130307-142308: The Baumslag-Solitar group is non-Hopfian (2).

130307-135458: The Baumslag-Solitar group is non-Hopfian. (more...)

130227-161949: Hopfian groups.

130215-140130: Matrices and quadratics.

130213-165727: Meta-conjugacy-classes.

121218-150646: Kanenobu's conjecture (2).

121218-144311: Kanenobu's conjecture. (more...)

121211-143453: Knots that are ribbon in multiple ways.

121121-153420: Triangulations and multi-curves (2).

121114-165832: Triangulations and multi-curves.

121101-084420: $\pi_2$ and ribbon braids.

121031-164550: The fundamental group of a non-ribbon 2-knot.

121024-153737: A non-ribbon 2-knot.

121003-152900: Is ${\mathcal K}^{bh}_{\text{all}}$ a finitely generated MGA?

120919-170659: September 19 notes.

120905-154614: There is a knotted 4-punctured sphere whose boundary is the unlink, but there isn't such a 3-punctured sphere.

120821-152726: Untangled stack presentations.

120807-151732: One-line stack presentations (3).

120731-171704: One-line stack presentations (2).

120731-165500: Analyzing the Carter-Saito 2-knot (3).

120731-164442: Analyzing the Carter-Saito 2-knot (2).

120731-163914: Analyzing the Carter-Saito 2-knot.

120724-155713: One-line stack presentations.

120716-155118: Plumbing in ${\mathbb R}^4$ (2).

120704-152002: Plumbing in ${\mathbb R}^4$.

120628-165934: Stack presentations (8), and the $\pi_1$ and $\pi_2$ story.

120618-152703: Stack presentations (7).

120525-134509: Stack presentations (6).

120517-160250: Stack presentations (5).

120517-153600: Stack moves to R moves.

120510-161654: Stack presentations (4).

120510-151741: Stack presentations (3).

120503-160037: Stack presentations (2).

120426-153125: Stack presentations.

120406-133930: Spinning a ribbon 1-knot.

120406-120255: The Nakanishi-Nakagawa example (14).

120406-120206: The Nakanishi-Nakagawa example (13).

120406-120115: The Nakanishi-Nakagawa example (12).

120406-120013: The Nakanishi-Nakagawa example (11).

120406-115826: The Nakanishi-Nakagawa example (10).

120406-115731: The Nakanishi-Nakagawa example (9).

120406-115635: The Nakanishi-Nakagawa example (8).

120406-115341: The Nakanishi-Nakagawa example (7).

120406-115200: The Nakanishi-Nakagawa example (6).

120406-114822: The Nakanishi-Nakagawa example (5).

120406-114626: The Nakanishi-Nakagawa example (4).

120406-114516: The Nakanishi-Nakagawa example (3).

120406-114331: The Nakanishi-Nakagawa example (2).

120406-114229: The Nakanishi-Nakagawa example.

120406-113653: A word-presentation for w-knots.

120327-090626: Seifert surfaces and ribbon knots.

120326-130432: SC Meeting.

120209-161652: The paper by Travis Schedler (5)

120203-092039: The paper by Travis Schedler (4)

120202-154639: The paper by Travis Schedler (3)

120123-175516: The paper by Travis Schedler (2)

120120-150234: The paper by Travis Schedler (more...)

111215-164429: The bracket in the Lie bi-algebra of curves (2).

111209-141446: The bracket in the Lie bi-algebra of curves.

111201-165327: A chord-diagram algorithm to decide the simplicity of plane curves.

111125-160312: Surfaces with circle boundary (2).

111117-182218: Surfaces with circle boundary.

111110-180409: Homotoping plane curves.

111104-103416: Turning ribbon singularities into clasp singularities.

111004-162300: Reading Blake Winter.

110923-170815: A hyperbolic picture of the free group.

110630-160804: PairingCycles.

110623-160414: The Turaev Quantization (2).

110623-152836: The Turaev Quantization. (more...)

110616-154345: Simplifying crossingless virtual knots.

110607-155801: The two types of forced intersections.

110512-151854: Obstructions to planarity.

110505-153348: The Lie Bialgebra of Curves.

110419-140741: Kuratowski-style obstructions to simplicity of curves.

110413-145804: Some quotients of the hyperbolic plane.

110413-142856: The Birman-Series Simplicity Algorithm (2).

110329-142547: The Birman-Series Simplicity Algorithm. (more...)

110322-152236: Planar curves and free groups (2).

110322-145141: Planar curves and free groups.

110310-140400: Planarity of curves (2).

110308-164010: Planarity of curves. (more...)

110222-143847: A w-Borromean braid.

110208-150040: Combinatorial planes and Artin's theorem.

110127-143209: Questions on planar representations of braids (2).

110111-135253: Finite type for Catalans.

110111-132853: Questions on planar representations of braids.

101218-140640: Planar Morse curves (3).

101208-162356: Planar Morse curves (2).

101202-170249: Planar Morse curves.

101125-171326: Simple curves in the n-punctured disk (3).

101118-172850: Simple curves in the n-punctured disk (2).

101111-180032: Simple curves in the n-punctured disk.

101028-171722: Claspers.

101022-090322: Reading Belavin-Drinfel'd.

101014-175219: Manin triples and the "big bracket". (more...)

100930-174525: Some basics of Lie bialgebras (3).

100930-171830: Some basics of Lie bialgebras (2).

100924-121247: Some basics of Lie bialgebras.

100826-134508: R2-trivial plane curves.

100819-160557: A non-realizable circle diagram.

100813-141103: Gauss diagrams for ribbon handlebodies.

100813-135437: Ribbon diagrams, ribbon handlebodies and Gauss diagrams for immersed surfaces.

100805-151028: Gauss diagrams for immersed surfaces.

100805-144347: Broken surfaces and ribbon handlebodies (2).

100729-170308: Broken surfaces and ribbon handlebodies. (more...)

100714-141059: The duality between the coefficients of the Alexander polynomial and wheels.

100714-133508: The bialgebra of ribbon knots.

100707-114711: The star presentation, cycles and wheels.

100630-152252: The star presentation.

100630-150302: Review of finite-type.

100630-144741: Moves on ribbon handlebodies. (more...)

100525-150826: Renormalizing the Alexander polynomial.

100525-142135: Review of the Alexander polynomial.

100517-150612: The Alexander polynomial of a ribbon 2-knot is of finite type.

100517-145200: The Alexander polynomial of a ribbon 2-knot.

100517-143734: The fundamental group of a ribbon 2-knot (2).

100517-142417: The fundamental group of a ribbon 2-knot.

100510-144232: The definition of finite type.

100510-143120: The definition of ribbon 2-knots (2).

100510-141822: The definition of ribbon 2-knots. (more...)