Morse-Bott theory on posets and a homological Lusternik-Schnirelmann theorem

被引：0

作者：

Fernandez-Ternero, D. ^{[1
]}

Macias-Virgos, E. ^{[2
]}

Mosquera-Lois, D. ^{[2
]}

Vilches, J. A. ^{[1
]}

机构：

[1] Univ Seville, Dept Geometria & Topol, Seville, Spain

[2] Univ Santiago de Compostela, Inst Matemat, Santiago De Compostela, Spain

来源：

JOURNAL OF TOPOLOGY AND ANALYSIS | 2024年 / 16卷 / 03期

关键词：

Morse-Bott functions; posets; Lusternik-Schnirelmann theorem; CATEGORY;

D O I：

10.1142/S1793525321500709

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop Morse-Bott theory on posets, generalizing both discrete Morse-Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik-Schnirelmann theorem for general matchings on posets, in particular, for Morse-Bott functions.

引用

页码：323 / 346

页数：24

共 28 条

[21] Lusternik-Schnirelmann category and algebraic R-local homotopy theory
Scheerer, H
Tanre, D
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1998, 50 (04): : 845 - 862
[22] Axiomatic S1 Morse-Bott theory
Hutchings, Michael
Nelson, Jo
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2020, 20 (04): : 1641 - 1690
[23] A LUSTERNIK-SCHNIRELMANN TYPE THEOREM FOR LOCALLY LIPSCHITZ FUNCTIONALS WITH APPLICATIONS TO MULTIVALUED PERIODIC PROBLEMS
RADULESCU, VD
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1995, 71 (07) : 164 - 167
[24] Strong Discrete Morse Theory and Simplicial L–S Category: A Discrete Version of the Lusternik–Schnirelmann Theorem
Desamparados Fernández-Ternero
Enrique Macías-Virgós
Nicholas A. Scoville
José Antonio Vilches
Discrete & Computational Geometry, 2020, 63 : 607 - 623
[25] EXISTENCE OF EIGENVALUES FOR ANISOTROPIC AND FRACTIONAL ANISOTROPIC PROBLEMS VIA LUSTERNIK-SCHNIRELMANN THEORY
Dussel, Ignacio ceresa
Bonder, Julian fernandez
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2024, 64 (02) : 577 - 596
[26] Some remarks on Morse theory for posets, homological Morse theory and finite manifolds
Gabriel Minian, Elias
TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (12) : 2860 - 2869
[27] A gap theorem for Lusternik-Schnirelmann π1-category (vol 93, pg 35, 1999)
Matumoto, Takao
TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (11) : 1956 - 1958
[28] REMARKS ON THE PROBLEM OF REGULAR PRIMES FOR H-SPACES - APPLICATION TO A MAPPING-THEOREM FOR LUSTERNIK-SCHNIRELMANN CATEGORY
SCHEERER, H
PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1987, 90 (03): : 319 - 324

← 1 2 3 →