[MBw] [w] [w] 390-8621 쌧{s3-1-1 ǗҁF \ ---ksakai(at)math.shinshu-u.ac.jp

[ u\ ] [ ܂ł̍u ] [ Algebraic Toplogy: A guide to literature ] [ English ]

# u\

ځF Torsion in the space of commuting elements in a Lie group c Liswj ̃Z~i[̓ICŊJÂ܂D Q܂́C̃tH[炲o^D Let $$\mathrm{Hom}(\mathbb{Z}^m,G)$$ denote the space of commuting $$m$$-tuples in a Lie group $$G$$. This space is identified with the based moduli space of flat bundles over a torus, so it is an important object not only in topology but also in geometry and physics. I will talk about torsion in the homology of $$\mathrm{Hom}(\mathbb{Z}^m,G)$$. We prove that for $$m\geq 2$$, $$\mathrm{Hom}(\mathbb{Z}^m,SU(n))$$ has $$p$$-torsion in homology if and only if $$p\leq n$$. The proof includes a new homotopy decomposition of $$\mathrm{Hom}(\mathbb{Z}^m,G)$$ in terms of a homotopy colimit. This talk is based on the joint work with Daisuke Kishimoto.
ځF Smooth CW ComplexWhitney Approximation ␣ viBwj ̃Z~i[̓ICŊJÂ܂D Q܂́C̃tH[炲o^D CW complexDiffeology̌ɎRɖߍނƂł邪CRȂǂ\͎CႦΑl̂̂Ȃ[Ƃ͑SقȂꏊɂD ̈ől̂̋ɂ߂Smooth CW complex\łCde Rham̒藝𖞂ɗǂ̂ł邱ƂĂD ́C^ꂽCW complexɑ΂ăzgs[lismooth zgs[lƂ͂ȂȂjƂȂSmooth CW complex݂邱ƂWhitney ApproximationpĎD ܂lȋc_ɂSmooth CW complexCӂ̊J핢ɑ΂1̕C܂\smooth functionƂD
ځF Parametrized motion planning and micro-tourism c NiMBwj ̃Z~i[̓ICŊJÂ܂D Q܂́C̃tH[炲o^D NCRiЂɂoςւ̑Ō[𑝂CɊόƂ͐sȂقǂɗłD ̊όƂ񕜂̕ƂāCu}CNc[YvƌĂ΂ߗׂւ̊όĂъ|񌾂ڂĂD {uł́C}CNc[Y̎_ɊÂCijׂȂړ[gw肷ASY̗_IȑʂTD ́CCohen-Farber-Weinbergerɂ2020Nɓꂽp[^[[V݌vCCŴȂǂposet-stratified spaceɓKp邱ƂɂCꂽ̈œ삷AȌoHwASY̕Kvŏɒڂ̂łD ̗ƂẮCʁCg[XCˉeԏ̎RȖĚ̕vZɂĂЉD
ځF TBA Jongbaek Song (Korea Institute for Advanced Study) ̃Z~i[̓ICŊJÂ܂D TBA
ځF TBA ጎ xiMBwj ̃Z~i[̓ICŊJÂ܂D TBA

# 2021Nx̍u

ځF $$\mathcal{L}$$-fillablêƂ|whv_Ng̒̃zCgwbhςɂ g iBwj ̃Z~i[̓ICŊJÂ܂D
ځF Tverberg's theorem for cell complexes ݖ{ Siswj ̃Z~i[̓ICŊJÂ܂D
ځF A comparison between two de Rham complexes in diffeology I FiMBwj ̃Z~i[̓ICŊJÂ܂D
ځF KneserOtƋʂKroneckerd핢Otɂ Oiwj ̃Z~i[̓ICŊJÂ܂D
ځF Bottl̂HirzebruchȖʑ Γc Tiwj ̃Z~i[̓ICŊJÂ܂D